A209702 Triangle of coefficients of polynomials v(n,x) jointly generated with A209701; see the Formula section.

1, 2, 3, 3, 5, 7, 4, 8, 16, 17, 5, 12, 30, 47, 41, 6, 17, 50, 99, 134, 99, 7, 23, 77, 181, 315, 373, 239, 8, 30, 112, 302, 628, 968, 1020, 577, 9, 38, 156, 472, 1128, 2090, 2898, 2751, 1393, 10, 47, 210, 702, 1882, 4020, 6738, 8495, 7338, 3363, 11, 57

Offset

1,2

Comments

For a discussion and guide to related arrays, see A208510.

Links

Table of n, a(n) for n=1..57.

Formula

u(n,x)=x*u(n-1,x)+x*v(n-1,x),

v(n,x)=2x*u(n-1,x)+(x+1)v(n-1,x)+1,

where u(1,x)=1, v(1,x)=1.

Example

First five rows:
1
2...3
3...5....7
4...8....16...17
5...12...30...57...41
First three polynomials v(n,x): 1, 2 + 3x , 3 + 5x + 7x^2.

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]  (* A209701 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]  (* A209702 *)

Crossrefs

Cf. A209701, A208510.

Sequence in context: A333295 A081493 A144680 * A077558 A122444 A373751

Adjacent sequences: A209699 A209700 A209701 * A209703 A209704 A209705

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 12 2012

Status

approved